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Exploiting Set-Based Structures to Accelerate Dynamic Programming Algorithms for the Elementary Shortest Path Problem with Resource Constraints

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Abstract

In this paper we consider a label-setting dynamic-programming algorithm for the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). We use a pseudo resource to guarantee that labels are permanent. We observe that storing the states based on the subset of nodes visited by the associated path can improve the performance of the algorithm significantly. To this end we use a variant of a prefix tree to store the states and show by computational experiments that the performance of the dynamic programming algorithm is improved significantly when the number of undominated states is large.

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  • Range, Troels Martin, 2013. "Exploiting Set-Based Structures to Accelerate Dynamic Programming Algorithms for the Elementary Shortest Path Problem with Resource Constraints," Discussion Papers of Business and Economics 17/2013, University of Southern Denmark, Department of Business and Economics.
  • Handle: RePEc:hhs:sdueko:2013_017
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    File URL: http://static.sdu.dk/mediafiles//F/9/4/%7BF94B03F2-40D0-4E96-AD02-86C70DD2B393%7Ddpbe17_2013.pdf
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    1. Santos, Luis & Coutinho-Rodrigues, João & Current, John R., 2007. "An improved solution algorithm for the constrained shortest path problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 756-771, August.
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    Keywords

    Elementary shortest path problem; resource constraints; dynamic programming; prefix tree;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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